Beam Quality Factor M²
M² = (π w₀ θ)/λ. M² = 1 for ideal Gaussian, higher for multimode beams.
M² = π w₀ θ / (2λ)
1.476
1 for a TEM₀₀ Gaussian
Beam parameter product w₀θ/2
0.5000 mm·mrad
TEM₀₀: λ/π = 0.3387 mm·mrad
TEM₀₀ divergence (full angle)
1.355 mrad
2λ/(πw₀) for the same waist
Rayleigh range πw₀²/(M²λ)
500.0 mm
Beam radius around the waist for the same w₀
- M² = 1
- M² = 2
- M² = 5
- This beam, M² = 1.48
Model and references
Exact. The equations are exact within the stated assumptions, or are a standard's tabulated values. The results are as good as the inputs. About the tiers
M² from the second-moment waist radius and far-field half angle, as ISO 11146 defines it. The result is only as good as the widths: a 1/e² or knife-edge width of a non-Gaussian beam gives a different M².
- Siegman A. E. (1990). New developments in laser resonators. Proc. SPIE 1224, 2. doi:10.1117/12.18425
- ISO 11146-1:2021. Lasers and laser-related equipment: test methods for laser beam widths, divergence angles and beam propagation ratios, part 1.